To get the missing terms, we must completely factorize the Left Hand Side of the Equation.
We can do this in two different ways
<u>Method 1</u>
![100x^{2} -36= 4(25x^{2} -9)}](https://tex.z-dn.net/?f=100x%5E%7B2%7D%20-36%3D%204%2825x%5E%7B2%7D%20-9%29%7D)
![\Rightarrow 100x^{2} -36= 4((5x)^{2} -3^2)}](https://tex.z-dn.net/?f=%5CRightarrow%20100x%5E%7B2%7D%20-36%3D%204%28%285x%29%5E%7B2%7D%20-3%5E2%29%7D)
Using difference of two squares we have
![\Rightarrow 100x^{2} -36= 4(5x+3)(5x-3)}](https://tex.z-dn.net/?f=%5CRightarrow%20100x%5E%7B2%7D%20-36%3D%204%285x%2B3%29%285x-3%29%7D)
By comparing to the given equation, the missing term is
![3](https://tex.z-dn.net/?f=3)
<u>Method 2</u>
![100x^{2} -36](https://tex.z-dn.net/?f=100x%5E%7B2%7D%20-36)
![\Rightarrow 100x^{2} -36= (10x)^{2} -6^{2}](https://tex.z-dn.net/?f=%5CRightarrow%20100x%5E%7B2%7D%20-36%3D%20%2810x%29%5E%7B2%7D%20-6%5E%7B2%7D)
Recall and apply the difference of two squares formula, to obtain,
![100x^{2} -36=(10x+6)(10x-6)](https://tex.z-dn.net/?f=%20100x%5E%7B2%7D%20-36%3D%2810x%2B6%29%2810x-6%29)
We can still further factor 2 out of each factor to get,
![100x^{2} -36=2(5x+3) \times 2(5x-3)](https://tex.z-dn.net/?f=100x%5E%7B2%7D%20-36%3D2%285x%2B3%29%20%5Ctimes%202%285x-3%29)
![\Rightarrow 100x^{2} -36=2\times2(5x+3)(5x-3)](https://tex.z-dn.net/?f=%5CRightarrow%20100x%5E%7B2%7D%20-36%3D2%5Ctimes2%285x%2B3%29%285x-3%29)
![\Rightarrow 100x^{2} -36=4(5x+3)(5x-3)](https://tex.z-dn.net/?f=%5CRightarrow%20100x%5E%7B2%7D%20-36%3D4%285x%2B3%29%285x-3%29)
By comparing to the given equation, the missing term is
![3](https://tex.z-dn.net/?f=3)